Convective Cahn-Hilliard models: from coarsening to roughening

In this paper we demonstrate that convective Cahn-Hilliard models, describing phase separation of driven systems (e.g., faceting of growing thermodynamically unstable crystal surfaces), exhibit, with the increase of the driving force, a transition from the usual coarsening regime to a chaotic behavior without coarsening via a pattern-forming state characterized by the formation of various stationary and traveling periodic structures as well as structures with localized oscillations. Relation of this phenomenon to a kinetic roughening of thermodynamically unstable surfaces is discussed.